When you use an inquiry-based approach in your classroom, students discover mathematical properties for themselves. Instead of presenting students with a theorem, formula, or rule, you guide them through an investigation. Inquirylearning is often done in a hands-on way.

Inmy inquiry lessons, I like to have students write patterns and observations in complete sentences, then develop a rule for the property they have observed. This helps them to internalize what is happening. Then, I lead them into writing a mathematical formula or rule to represent their words.

The students learn to look for connections.They also develop valuable skills such as the ability to self-direct and the ability to clearly express their discoveries in both words and mathematical language.

1. Inquiry enhances independent problem solving skills.

Inquiry-based learning teaches students how to find patterns, figure out properties, and discover new rules of mathematics. They slowly learn how their brain actually progresses through the idea to get them from "lost" to "ohhhhh, I see what the pattern is." After this becomes second nature, they will be more ready to attack future unknown situations.

The critical thinking skills that are required to ask questions that will lead to discovery are learned and acquired. They develop through practice, just like any other skill. Students must practice the inquiry process, just like we as teachers must practice sitting back and letting them struggle. It's not easy, but begins to feel more natural over time.

As students get more and more accustomed to the inquiry structure that you use, they will slowly strengthen their own skills and gain independence in problem solving.

Here's an Algebra example:
I always teach exponent rules with guided inquiry. We work through the patterns and write out all the variables and cancel or expand until students develop product rule, power rule, and quotient rule for themselves. Then, when we get to the negative exponents later in the unit, their skills with this process have grown to the point that they know how to come up with their own concrete examples. They know how to look for patterns. I have them develop their own sets of rules for negative exponents.

Work towards the skills that will lead your students to persistence in problem solving.

2. Discovery leads to deeper understanding of a specific concept.

After discovering a mathematical property on their own, students will truly understand the concept behind the rule. Instead of following a set procedure, they will understand WHY a rule works and HOW it was developed.

Let your students build a concept, not just follow a given process.

It's very rare that I give a formula as a part of notes. I like to have students find a formula for themselves. One example is for surface area of a cylinder. I have a dissection lesson for classes to "dissect" a cylinder "specimen."

They have to discover for themselves that the length of the rectangle is equal to the circumference of the circle, and then go from there. Most middle school students across the world REALLY struggle with truly understanding this formula. They have a hard time visualizing the base and why circumference plays a part in this formula. However, after this hands-on lesson, the students really "get it" and never forget how the rectangular face wraps around. You can read more about this lesson in my Cylinder Dissection blog post.

I do a similar structure for discovering circle theorems in High School Geometry. Students draw their own chords and have to tell ME how arcs, tangents, central angles, and inscribed angles are related, instead of me telling THEM these theorems.

3. Students discover a new level of math confidence & self-motivation.

When students feel the pride that comes from discovering a theorem, property, or formula for themselves (just like a mathematician does!), they suddenly gain a new level of confidence in their own math abilities.

I have noticed students have a sudden willingness to try a new challenge or approach a different type of problem instead of giving up. Kids believe in their ability to apply knowledge from one situation to another.

I feel like this has given my students huge advantages on standardized tests. After I started incorporating more and more inquiry learning, the kids got more and more comfortable with being exposed to an unfamiliar problem type.

This is so important to note, and one of the benefits that I rarely see advertised by supporters of inquiry learning. Here's the thing:

If a student develops a formula, rule, or property for himself, then he understands on a deeper level where it came from. He won't have to memorize it at all.

The student can reproduce the formula at any time because he "discovered" it. This is especially true if it was done in a hands-on way.

During a test, or later in life, the development of the idea is what will help a student recall how a property works or how to re-create the formula.

So, here's how to make it happen in your classroom:

Some tips as you start to incorporate more inquiry learning, and give your students these benefits -

Sit back. Don't jump in to help. Let students struggle through the first few inquiry lessons. It's so hard to resist giving hints, but do your best to choose when to give assistance and who to offer it to. They will get used to this process and it will really be best for them in the long run. Help those who truly need it, but otherwise, let them develop their own skills. Stick with it. It will get easier!

Never (or very rarely) GIVE your students a rule or formula. Get out of the habit of feeding information and properties to them. For example, if you currently teach rules of divisibility, twist the lesson to have the kids find the rules and present them to you.

Require your students to write up their observations in complete sentences. Follow up all inquiry lessons with a full written explanation. Give your kids the benefits that come from working to explain the properties that were discovered in their own words. Then, also have them translate into mathematical language to develop the formula as well.

Have students share both their questioning process and discoveries aloud. They can work in pairs or small teams or they can present findings to the class. Allow them to collaborate and share the strategies they used to figure out the property. Encourage metacognition!

Plan carefully so that your students do have enough guidance to succeed. Try a consistent structure like my SPORT method for structuring inquiry so that they know what to expect and can thrive in inquiry learning.

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I am a student support specialist teacher, and I find that this is simply wonderful. I am not a math specialist so I can understand and empathise as to why my students have such difficulty with Maths and the different styles of teaching it. Thank you, I hope to do some mini sessions with groups of teachers, this is just perfect.

Hi Julie,
Thanks so much! I'm excited to hear that you might share some of this with groups of teachers. That's awesome! Thank you for your comment!
- Brigid

Reply

Anne DeArmon

10/27/2017 09:15:18 pm

I am using a program called Mathematics Vision Project this year. It is almost all inquiry based. I have always said this would be the most fun way to teach math. However I am truly sold on it now. I have been teaching how to complete the square for many years. Up to this year I have basically given a step by step way of showing the students and constantly had to repeat the process. This year we did a inquiry based way using a concept of quilt squares. By the second lesson the students were telling me how to do it. I believe a majority of the class had it figured out and were working on problems on their own without repetition of steps, not that I had to give steps anyway.
I would love to pass this article onto parents.